I have no idea who sings it, or what the title is, but it is very angry heavy/speed metal ( no idea) and all the lyrics, from what I could discern were, " I hate you. I hate you. I hate you. I hate you…"
So, I suppose the name of the song is I Hate You.
The Salt In My Tears by Martin Briley. Break-up songs don’t get much better than this!
Haven’t thought of that song in years (decades, even)! Off to iTunes now! 
Well some things you can explain away
But the heartache’s in me til this day
Did you stand by me? No not at all
Did you stand by me? No way
Train in Vain by the Clash. Although it’s from the man’s perspective, it rocks.
HOW did I not think of that one?! Hell, it’s in my standard shuffle playlist…
I’ve always been partial to Happy Break-Up Song by NOFX. From a guy’s perspective, but oh well.
Things by Paul Westerberg
This is what I came in to mention. It’s the best breakup song ever.
My favorite thread on the subject